| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Particle on rough horizontal, string over pulley |
| Difficulty | Moderate -0.8 This is a standard connected particles problem with straightforward application of Newton's second law. Parts (a)-(c) involve routine mechanics: writing F=ma equations for each particle, solving simultaneous equations for acceleration, and using kinematics (s=ut+½at²). The friction force is given explicitly, eliminating any need to calculate it. Part (d) requires basic modeling awareness. This is easier than average A-level content as it's a textbook exercise with no problem-solving insight required. |
| Spec | 3.03b Newton's first law: equilibrium3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Equation of motion for \(A\): \(T - 12.7 = 2.5a\) | M1, A1 | AO3.3, AO1.1b — resolving horizontally for \(A\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Equation of motion for \(B\): \(1.5g - T = 1.5a\) | M1, A1 | AO3.3, AO1.1b — resolving vertically for \(B\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Solving two equations for \(a\) | M1 | AO1.1b — complete correct strategy, setting up two equations in \(a\) and solving |
| \(a = 0.5\) | A1 | AO1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(1 = \frac{1}{2} \times 0.5 \, t^2\) | M1 | AO3.4 — complete method (may use more than one suvat formula) to give equation in \(t\) only |
| \(t = 2\) seconds | A1ft | AO1.1b — ft from their \(a\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Valid improvement (first) | B1 | AO3.5c |
| Valid improvement (second) | B1 | AO3.5c — any two of: include dimensions of ball; include dimensions of pulley so string not parallel to table; include variable resistance instead of constant; use more accurate value for \(g\) |
## Question 9(a)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Equation of motion for $A$: $T - 12.7 = 2.5a$ | M1, A1 | AO3.3, AO1.1b — resolving horizontally for $A$ |
## Question 9(a)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Equation of motion for $B$: $1.5g - T = 1.5a$ | M1, A1 | AO3.3, AO1.1b — resolving vertically for $B$ |
## Question 9(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Solving two equations for $a$ | M1 | AO1.1b — complete correct strategy, setting up two equations in $a$ and solving |
| $a = 0.5$ | A1 | AO1.1b |
## Question 9(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $1 = \frac{1}{2} \times 0.5 \, t^2$ | M1 | AO3.4 — complete method (may use more than one suvat formula) to give equation in $t$ only |
| $t = 2$ seconds | A1ft | AO1.1b — ft from their $a$ |
## Question 9(d):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Valid improvement (first) | B1 | AO3.5c |
| Valid improvement (second) | B1 | AO3.5c — any two of: include dimensions of ball; include dimensions of pulley so string not parallel to table; include variable resistance instead of constant; use more accurate value for $g$ |9.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{8f3dbcb4-3260-4493-a230-12577b4ed691-18_694_1262_223_406}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}
A small ball $A$ of mass 2.5 kg is held at rest on a rough horizontal table.\\
The ball is attached to one end of a string.\\
The string passes over a pulley $P$ which is fixed at the edge of the table. The other end of the string is attached to a small ball $B$ of mass 1.5 kg hanging freely, vertically below $P$ and with $B$ at a height of 1 m above the horizontal floor.
The system is release from rest, with the string taut, as shown in Figure 2.\\
The resistance to the motion of $A$ from the rough table is modelled as having constant magnitude 12.7 N . Ball $B$ reaches the floor before ball $A$ reaches the pulley.
The balls are modelled as particles, the string is modelled as being light and inextensible, the pulley is modelled as being small and smooth and the acceleration due to gravity, $g$, is modelled as being $9.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Write down an equation of motion for $A$.
\item Write down an equation of motion for $B$.
\end{enumerate}\item Hence find the acceleration of $B$.
\item Using the model, find the time it takes, from release, for $B$ to reach the floor.
\item Suggest two improvements that could be made in the model.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 2 Q9 [10]}}